Event-based H∞ consensus control for second-order leader-following multi-agent systems

By using the event-based strategy, the H∞ consensus problem of second-order leader-following multi-agent systems with a directed communication network graph is investigated. Firstly, this paper provides a distributed event-triggered sampling scheme and an event-based distributed sampling rules by using algebraic graph theory and matrix theory, and proposes a sufficient condition under reasonable assumptions for solving the H∞ consensus problem of second-order leader-following multi-agent systems. Secondly, in order to reduce the conservatism of the given condition, two equivalent improved conditions by using the linear matrix inequality (LMI) theory are established. Thirdly, considering a special case of the external disturbance, a new event-based distributed sampling rule is provided, which can reduce the update of controller and completely exclude the Zeno-behavior. Fourthly, consider the consensus problem as a special situation of H∞ consensus problem when the value of the external disturbance is zero, and make all the obtained results of H∞ consensus problem extend to the consensus problem. Finally, two numerical examples are given to demonstrate the effectiveness of theoretical results.